where \(\hat{\mathbf {\beta }}\)  needs to be computed. [1]} estimates \(\hat{\mathbf {\beta }}\)  by solving the following regression problem:
\(\hat{\mathbf {\beta }} = \mathop {\arg \min }_{\mathbf {\beta }} \mathbb {E}_{\mathbf {x}^{(1)}, \ldots , \mathbf {x}^{(N)} \overset{\text{i.i.d.}}{\sim }p_{\mathbf {x}}(\mathbf {x})} \bigg \Vert \frac{\sum _{j=1}^{N}\exp \big (\mathbf {\beta }^\top \mathbf {\gamma }(\mathbf {x}^{(j)})\big )\mathbf {\gamma }(\mathbf {x}^{(j)})}{\sum _{j^{\prime }=1}^{N}\exp \big (\mathbf {\beta }^\top \mathbf {\gamma }(\mathbf {x}^{(j^{\prime })})\big )} - \mathbf {\mu }\bigg \Vert _2^2.\) 
